Finite Group Databasebeta

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C₂₉×#2453 #16816167

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(34,35,38,41)(36,40,37,39)(43,47)(45,48);(31,33)(34,36,38,37)(35,39,41,40)(42,43)(44,48)(45,49)(46,47);(30,31)(32,33)(34,35)(36,39)(37,40)(38,41)(42,44,46,49)(43,48,47,45);(34,37,38,36)(35,40,41,39)(42,45,46,48)(43,49,47,44)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1185);